Question: $A$ $B$ $C$ If: $ BC = 6x + 4$, $ AC = 52$, and $ AB = 4x + 8$, Find $BC$.
From the diagram, we can see that the total length of ${AC}$ is the sum of ${AB}$ and ${BC}$ $ {AB} + {BC} = {AC}$ Substitute in the expressions that were given for each length: $ {4x + 8} + {6x + 4} = {52}$ Combine like terms: $ 10x + 12 = {52}$ Subtract $12$ from both sides: $ 10x = 40$ Divide both sides by $10$ to find $x$ $ x = 4$ Substitute $4$ for $x$ in the expression that was given for $BC$ $ BC = 6({4}) + 4$ Simplify: $ {BC = 24 + 4}$ Simplify to find ${BC}$ : $ {BC = 28}$